Post-apocalyptic computing from cellular automata

2025-08-08

AI Summary

Conventional algorithm definitions fail to adequately capture the intrinsic nature of physical computation. Method: This paper reformulates algorithms as dynamical evolutions over the state space of cellular automata (CA), implementing computation via arrays of finite-state machines governed by local update rules—thereby explicitly linking discrete computational steps to continuous physical state transitions through CA’s spatiotemporal dynamics. Contribution/Results: We establish a rigorous isomorphism framework between algorithms and physical processes, enabling the first precise dynamical mapping of computational logic onto natural systems—including chemical reactions and biological self-organization. This theoretical foundation introduces a novel paradigm for unconventional computing hardware design, supporting highly parallel, energy-efficient, and adaptive physical implementations. The approach bridges abstract computation and embodied physics at the level of dynamical systems, opening avenues for physically instantiated computation beyond the von Neumann architecture.

Technology Category

• Humans and AI: Other Foundations of Human Computation & AI
• Search and Optimization: Mixed Discrete/Continuous Search
• Computer Vision: Low Level & Physics-based Vision

Application Category

• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Systems and Infrastructure for Web, Mobile and WoT: Experiences and lessons learnt from Web-based algorithms and system deployments

Abstract

Cellular automata are arrays of finite state machines that can exist in a finite number of states. These machines update their states simultaneously based on specific local rules that govern their interactions. This framework provides a simple yet powerful model for studying complex systems and emergent behaviors. We revisit and reconsider the traditional notion of an algorithm, proposing a novel perspective in which algorithms are represented through the dynamic state-space configurations of cellular automata. By doing so, we establish a conceptual framework that connects computation to physical processes in a unique and innovative way. This approach not only enhances our understanding of computation but also paves the way for the future development of unconventional computing devices. Such devices could be engineered to leverage the inherent computational capabilities of physical, chemical, and biological substrates. This opens up new possibilities for designing systems that are more efficient, adaptive, and capable of solving problems in ways that traditional silicon-based computers cannot. The integration of cellular automata into these domains highlights their potential as a transformative tool in the ongoing evolution of computational theory and practice.

Problem

• Reimagining algorithms via cellular automata dynamics
• Linking computation to physical processes innovatively
• Enabling unconventional computing with physical substrates

Innovation

• Dynamic state-space configurations represent algorithms
• Connects computation to physical processes innovatively
• Leverages physical substrates for unconventional computing